Engineering Studies Data Book 2015 2014/47608 · 4 Engineering Studies Data Book 2015 . General formulae . Side lengths of a right triangular plane figure . ho a. 22 2 = + h

Engineering Studies Data Book updated December 2013

Engineering Studies Data Book

2015

wagnr

Typewritten Text

2014/47608

___________________________________________________________________________________________ 2 Engineering Studies Data Book 2015

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CORE CONTENT

Engineering Studies Data Book 2015 3

SI units

Quantity SI unit

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic temperature kelvin K

energy, work, quantity of heat joule J power, radiant flux watt W Celsius temperature degree Celsius °C area square metre m2 volume cubic metre m3 speed, velocity metre per second m s-1 acceleration metre per second squared m s-2 mass density kilogram per cubic metre kg m-3

Standard prefixes

Factor Prefix Symbol Factor Prefix Symbol

1012 tera T 10-3 milli m

109 giga G 10-6 micro μ

106 mega M 10-9 nano n

103 kilo k 10-12 pico p

Common constants

Item Symbol Value

Ratio of the circumference of a circle to its diameter (Pi) 3.14159

CORE CONTENT


General formulae

Side lengths of a right triangular plane figure

2 2 2 h o a= + h is the hypotenuse o is the opposite side a is the adjacent side

Angular relationships of a right triangular figure

acoshosinhotana

θ

θ

θ

=

=

=

θ is the angle h is the hypotenuse o is the opposite side a is the adjacent side

Perimeter of a circle [p] p dπ= d is the diameter

Area of a circle [A] 2πrA = r is the radius

Surface area of open ended cylinder [A] A dhπ=

d is the diameter h is the height

Volume of a cylinder [V] 2V r hπ= r is the radius h is the height

Surface area of a sphere [A]

2π4 rA = r is the radius

Volume of a sphere [V] 33

4 π rV = r is the radius

Density [ρ] of a material Vm

=ρ m is mass V is volume

Energy [E] PtE =

t is the time taken P is the power

Efficiency [η] % 100Output%

Inputη = ×

CORE CONTENT


Common constants

Item Symbol Value

Acceleration due to gravity g 9.80 m s–2

Selected material properties

Material Density kg m-3

Elastic (Young’s) modulus kN mm-2

Ultimate tensile * strength N mm-2

Yield stress

N mm-2

Electrical conductivity Ω-1m-1 × 106

Thermal conductivity

W m-1K-1

Structural steel 7850 200 470 250 13.0 46

Stainless steel 7600 200 860 502 1.35 16

Cast iron 7200 120 180 10.3 80

Wrought iron 7750 200 10.3 80

Aluminium 2710 70 150 95 37.7 237

Brass 8740 90 190 50 16.7 109

Copper 8930 112 210 70 59.5 401

Zinc 7130 108 200 13.8 16.8 116

Solder (60% lead, 40% tin) 9280 23.7 37 - 7.28 43.6

Concrete 2400 30 40

(compressive) 0.8

Concrete (steel reinforced) 0.8

Timber (parallel to grain) 12 105 0.16

Polypropylene 1240 4 19.7 – 80 50 0.13

Polycarbonate 1200 2.3 70 0.19

ABS plastics 2.3 40 48.3 2.34

Nylon 1160 2 – 4 75 45

Acrylic 1190 3.2 70 73.7 0.19

Glass 2500 69 3600 1.05

Diamond 3520 1000 50 000 2320

Gold 19 320 82 220 40 44.6 318

Ice 931 9.17.5@-5°C 85 2.25@-5°C

Water pure 1000

Sea water 1022

Petrol 740 0.15

Crude oil 800 0.15

* Unless noted as compressive strength.

MECHANICAL SPECIALIST FIELD


Basic formulae (Mechanical) 1

Parameter Formula Terms Mechanical Advantage [MA]

effort

load

FFMA =

Fload is the output force Feffort is the input force

Velocity Ratio [VR]

load

effort

ddVR =

deffort is the distance moved by the effort dload is the distance moved by the load

Velocity ratios in drive trains (for gear or pulley train ) [VR]

3

3

2

2

1

1

DF

DF

DFVR =

F1,2 and 3 are the followers D1,2 and 3 are the drivers (measured via number of teeth on gears or by pulley diameters)

Torque [τ] Frτ = F is the force r is the radius

Moment of a force [M] FdM =

F is the force d is the perpendicular distance

Stress[σ] or Pressure [p] σ =

F( p )A

F is the force A is the area

Strain [ε] LL

ε ∆=

ΔL is the change in length L is the original length

Young’s (Elastic) modulus [E]

σε

=E σ is the stress ε is the strain

Young’s (Elastic) modulus [E] expanded formula

LAFLE∆

=

F is the force A is the area ΔL is the change in length L is the original length

Factor of Safety [FS] FS=

gsafeworkin

UTS

σσ

σUTS is the ultimate tensile stress σsafeworking is the safe working stress

Acceleration [a] −=

v uat

v is the final velocity u is the initial velocity t is the time

Velocity [v] 2 2 2v u as= +

u is the initial velocity a is the acceleration s is the distance

Distance [s] 22

1 atuts += u is the initial velocity t is the time a is the acceleration

Force [F] maF = m is the mass a is the acceleration

Equilibrium conditions ∑ = 0M

0=∑ yF

∑ = 0xF

Σ is the ‘sum of’ M are the moments Fy are the vertical force components Fx are the horizontal force components

Equilibrium conditions (expanded) ACWMCWM Σ=Σ

)()( downFupF Σ=Σ )()( rightFleftF Σ=Σ

Σ is the ‘sum of’ CWM are clockwise moments ACWM are anticlockwise moments

SPECIALIST FIELD MECHANICAL


Basic formulae (Mechanical) 2

Parameter Formula Terms

Work [W] FsW = F is the force s is the distance moved

Power [P] Fv

tFsP ==

F is the force s is the distance t is the time taken v is the average velocity

Energy [E] PtE =

t is the time taken P is the power

Potential energy [Ep]

mghEp =

m is the mass g is the acceleration due to gravity h is the height

Kinetic energy [Ek] 22

1 mvEk =

m is the mass v is the velocity

Potential and kinetic energy conversion kp EE ∆=∆

Δ is the ‘change in’

Efficiency [η] % 100

Work done in moving load%

Work done by the effortη = ×

Work done in moving load is the output Work done by the effort is the input

Compound gear or pulley system [RPM]

input RPMoutput RPMVR

=

VR is the velocity ratio RPM is the revolutions per minute

Linear velocity of a gear or pulley system [v]

( ) ( )260

RPM r svt

π= =

r is the radius of the gear or pulley s is the distance travelled t is the time taken

Distance around a winch drum [s]

rs π2=

r is the radius of the drum

Selected SI units

Derived quantity

SI unit

Name Symbol Expression in terms of

other SI units

Expression in terms of

SI base units force newton N – m kg s-2 pressure, stress pascal Pa N m-2 m-1 kg s-2 energy, work, quantity of heat joule J N m m2 kg s-2 power, radiant flux watt W – m2 kg s-3

MECHANICAL SPECIALIST FIELD


Second moments of area

Shape Dimensions Second moment of area about centroidal axis

Rectangle solid section (vertical)

12

3bhI xx =

Circular solid section x x

D

64

4DI xxπ

=

Circular tube section

D

t

x x

64)( 44

ioxx

DDI −=π

Do = cylinder outside diameter Di = cylinder inside diameter

SPECIALIST FIELD MECHANICAL


Simple beams

Beam configuration

Maximum bending moment

Maximum deflection (y)

A B

F

AatFLBM =max

Here F is the single vertical point load.

BatEIFLy

xx3

3

=


max 2UDLF LBM at A=

Here FUDL= ωL which is the load per unit length (ω) times the length of the beam (L)

3

8UDL

xx

F Ly at BEI

=


C

A B

F

CatFLBM4max =


CatEI

FLyxx48

3

=


CatLFBM UDL

8max =


CatEI

LFYxx

UDL

3845 3

=


Terms:

L Length of beam between supports ω A uniformly distributed load per unit length

FUDL The product of the UDL’s applied load/unit length (ω) and the length of the beam (L) F An applied vertical point load E The elastic (Young’s) modulus of the material of the beam. Ixx The second moment of area of the beam section. A The left hand end of the beam B The right hand end of the beam C The mid-point of the beam

ELECTRICAL/ELECTRONIC SPECIALIST FIELD


Resistor colour codes

E12 Preferred values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 And decades (e.g. 100, 1000, 10 000, …..10 000 000) thereafter Example: 4 band colour code

Electrical formula wheel

band colour 1st band 2nd band multiplier

Black 0 1

Brown 1 1 10

Red 2 2 100

Orange 3 3 1000

Yellow 4 4 10 000

Green 5 5 100 000

Blue 6 6 1 000 000

Violet 7 7

Grey 8 8

White 9 9

tolerance band

Brown ± 1%

Red ± 2%

Gold ± 5%

Silver ± 10%

SPECIALIST FIELD ELECTRICAL/ELECTRONIC


Basic formulae (Electrical/Electronic)


Ohm’s law IRV = V is the voltage I is the current R is the resistance

Power law 22 VP VI I R

R= = =

P is the power I is the current V is the voltage R is the resistance

Electrical energy [Ee] VItEe = V is the voltage I is the current t is the time

Resistors in series 1 2tR R R= + + Rt is the total resistance

R1, R2, … are the individual resistances Resistors in parallel

1 2

1 1 1

tR R R= + +

Rt is the total resistance R1, R2, … are the individual resistances

Capacitors in parallel 1 2= + +C C C C is the total capacitance

C1, C2, … are the individual capacitances Capacitors in series

1 2

1 1 1= + +

C C C

C is the total capacitance C1, C2, … are the individual capacitances

Charge of capacitor =Q CV Q is the charge C is the capacitance V is the voltage

Potential dividers 1 2

11

1 2

22

1 2

= +

=+

=+

cc

cc

cc

V V VRV V

R RRV V

R R

Vcc is the total voltage across the resistor pair V1 is the voltage across resistor R1 V2 is the voltage across resistor R2

Transistor current gain C

FEB

IhI

= IC is the collector current IB is the base current

LED in series with a resistor

( )−= cc LED

LED

V VR

I

Vcc is the total applied voltage VLED is the voltage across the LED ILED is the current through the LED R is the series resistor

Transformers

P P S SV I V I=

Vs is the secondary voltage Vp is the primary voltage Ns is the number of turns in the secondary coil Np is the number of turns in the primary coil Ip is the primary current Is is the secondary current

Kirchoff’s first law 0=∑ I The sum of currents flowing toward that point is equal to the sum of currents flowing away from that point

Kirchoff’s second law 0∆ =∑ V The directed sum of the electrical potential differences around a closed loop in a circuit must be zero

S S

P P

V NV N

=



Diode symbol

Transistor symbol (bipolar NPN transistor)

SPECIALIST FIELD ELECTRICAL/ELECTRONIC


Diode models On ( ),= =D D on D FV V or V V

Check: 0>DI

Off 0 ADI = Check:

( ),<D D on FV V or V Transistor models (NPN BJT) Cut-off 0= =B CI I

Check: 0.7 VBEV <

Saturation 0.7 V0V

BE

CE

VV

==

Check:

( )

0

β

>

<

B

CFE

B

II or hI

Forward-active

( )0.7 VBE

C B C FE B

VI I or I h Iβ

=

= × = ×

Check: 00

>>

B

CE

IV

Selected SI units

Derived quantity

SI unit

Name Symbol Expression in terms of

other SI units

Expression in terms of

SI base units

frequency hertz Hz – s-1

power, radiant flux watt W – m2 kg s-3 electric charge, quantity of electricity coulomb C – s A

electric potential difference, electromotive force volt V W A-1 m2 kg s-3 A-1

capacitance farad F C V-1 m-2 kg-1 s4 A2 electric resistance ohm Ω V A-1 m2 kg s-3 A-2



Standard symbols

SPECIALIST FIELD SYSTEMS AND CONTROL


Logic symbols and their truth tables

AND Gate

OR GateNOT Gate

NAND Gate

NOR Gate

XOR Gate

A Q0 11 0

A B0 01 0

Q00

01

11

01

A B0 01 0

Q01

01

11

11

A B0 01 0

Q10

01

11

00

A B0 01 0

Q11

01

11

10

A B0 01 0

Q01

01

11

10

AA

A A

A A

B

B B

B B

Q

Q

Q

Q

Q

NAND Gate Equivalents

Output = A

Output = A +B Output = A . B

Output = A +B

Output = A . B

SYSTEMS AND CONTROL SPECIALIST FIELD


Standard symbols



Selected PICAXE microprocessor pin allocations

Flow chart symbols

SYSTEMS AND CONTROL SPECIALIST FIELD


7400 logic chip layouts

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7400

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7432

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7402

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7486

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7404

14 13 12 11 10 9 8

1 2 3 4 5 6 7GND

Vcc

7408

Electrical formula wheel



Basic formulae (Systems and control)


Ohm’s law IRV = V is the voltage I is the current R is the resistance

Power law 22 VP IV I R

R= = =

P is the power I is the current V is the voltage R is the resistance

Resistors in series 1 2tR R R= + + Rt is the total resistance

R1, R2, … are the individual resistances Resistors in parallel

1 2

1 1 1

t....

R R R= + +

Rt is the total resistance R1, R2, … are the individual resistances

Potential dividers 1 2

11

1 2

22

1 2

= +

=+

=+

cc

cc

cc

V V VRV V

R RRV V

R R

Vcc is the total voltage across the resistor pair V1 is the voltage across resistor R1 V2 is the voltage across resistor R2

Mechanical advantage [MA]

effort

load

input

output

FF

FF

MA ==

in in out outF d F d× = ×

Foutput , Fload is the output force Finput , Feffort is the input force

Distance moved [dr] rack of metre per teeth of n

srevolution of n pinion on teeth of n)r(d moved distance o

oo ×=

Velocity ratio of a gear or pulley [VR]

output

input

input

output

output

input

dd

ττ

vv

VR ===

in

out

NVRN

=

v is the input or output velocity 𝜏 is the input or output torque d is the distance moved of the input or output N is the speed of rotation of the input or output

Torque [τ] Frτ = F is the force r is the radius

Moment of a force [M] FdM =

F is the force d is the perpendicular distance

Efficiency [η] VRMA η =

MA is the mechanical advantage VR is the velocity ratio

End of Data Booklet

Copyright © School Curriculum and Standards Authority, 2013 This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an intranet, for non-commercial purposes by educational institutions, provided that it is not changed in any way and that the Authority is acknowledged as the copyright owner. Copying or communication for any other purpose can be done only within the terms of the Copyright Act or with prior permission of the Authority. Copying or communication of any third party copyright material contained in this document can be done only within the terms of the Copyright Act or with permission of the copyright owners. This document is valid for teaching and examining until 31 December 2015.

Published by the School Curriculum and Standards Authority of Western Australia 303 Sevenoaks Street Cannington WA 6107

TRIM 2014/47608

ACKNOWLEDGEMENTS Electrical relationships: Electrical formula wheel. Retrieved January, 2010,

from www.sengpielaudio.com/calculatorohm.htm#top

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Engineering Studies Data Book 2015 2014/47608 · 4 Engineering Studies Data Book 2015 . General formulae . Side lengths of a right triangular plane figure . ho a. 22 2 = + h